Mathman, I must admit the examples wallylutz gave are tricky--but notice how it's essential that there be a sequence involving a triple in the layout, and a curve ball double jump like a double lutz. I certainly never thought a skater would ever plan a non-axel double to occupy an entire jumping pass.

I knew triple-triple sequences could throw off my proposition but didn't consider them at the time that I was writing the original post. I'm working on a more comprehensive response at the moment.

I believe that the Triple-1Lo-3F or 3S is a fully fledged combo, not a sequence. (The rule change last year that made this possible was a pretty cool one -- I hope more skaters try it, especially with a flip at the end. I doubt if any ladies will try the flip version, though. I believe that Sasha Cohen did something like th Salchow one, back when it was classified as a sequence.), though.

Other than that, I think the idea is that the second jump of a triple-triple combo can only be a loop or a toe loop, because otherwise you are on the wrong foot to do your next jump.

Edited to add A combo means you go right up into the second jump off the landing edge of the first. A sequence is where you take a step ior hop in between. So, for instance, a 3Lz+3T+3Lo or a 2A+2T+3T is a perfectly good combination and not a "sequence" in ISU nomenclature.

Another reason that people mention for wanting to change the scoring of combos is that under the current rules a 2Lo+3Lo gets the same base value as a 3Lo+2Lo, even though the first one is harder.

I believe that the Triple-1Lo-3F or 3S is a fully fledged combo, not a sequence. (The rule change last year that made this possible was a pretty cool one -- I hope more skaters try it, especially with a flip at the end. I doubt if any ladies will try the flip version, though. I believe that Sasha Cohen did something like th Salchow one, back when it was classified as a sequence.), though.

Other than that, I think the idea is that the second jump of a triple-triple combo can only be a loop or a toe loop, because otherwise you are on the wrong foot to do your next jump.

Edited to add A combo means you go right up into the second jump off the landing edge of the first. A sequence is where you take a step ior hop in between. So, for instance, a 3Lz+3T+3Lo or a 2A+2T+2Lo is a perfectly good combination and not a "sequence" in ISU nomenclature.

So even if you land a jump in a non-standard landing edge--say wallylutz's example of a double loop landed on the inside edge of the opposite foot--and use that edge to take off for another jump it counts as a combo and not a sequence?

If so, could one-foot double axels be used to enter into a triple salchow or triple flip?

Last year ISU started allowing a half Loop as a second jump counted as a 1Lo to qualify a 3 jump sequence as a combo.

Patrick Chan and Lori Nichol immediately took advantage of this in rechoreographing the POTO Lp but he was only doing 3Lz/1Lo/2S until the Canadian Nationals when he did the 3/1/3 which is worth more than the previous 3/2/2. The landing of the first jump has to be just right so it's not quite so easy. Doing this combo also opened up another jump opportunity as Wallylutz explained before.

I am far from an expert on this, but I think the answer to both of your questions is yes.

(I am not sure whether this discussion is about mathematical possibliites involving the weirdest stuff we can imagine, or whether it is about things that someone might actually do.)

Haha. Well, my original point, which got sidetracked a bit, was that for any difficult layout involving one or more triple-triple combos, it is possible to rearrange the jumps in that layout to make it much easier to execute without reducing the base value. In particular, I had in mind removing the triple-triple combinations. (Hence the Triple-triple "penalty")

I believe my proposition still holds for layouts that don't have triple-triple sequences.

So even if you land a jump in a non-standard landing edge--say wallylutz's example of a double loop landed on the inside edge of the opposite foot--and use that edge to take off for another jump it counts as a combo and not a sequence?

Yes.

If so, could one-foot double axels be used to enter into a triple salchow or triple flip?

In theory, yes. They would be scored as combinations.

In practice, no one has ever done those combos in the past, so don't hold your breath waiting to see them any time soon.

Watch the weaker juniors and novices and below who don't do triple jumps, and maybe you'll occasionally see double something easier than axel-double salchow combinations with the first jump landed on an inside edge. Still rare, but it has been done in the past so more likely it'll be done again in the near future.

So even if you land a jump in a non-standard landing edge--say wallylutz's example of a double loop landed on the inside edge of the opposite foot--and use that edge to take off for another jump it counts as a combo and not a sequence?

Under the new rule for this season, yes. Didn't used to be that way, but that's the rule now.

And we've gone really far off track with some of the crazier scenarios people have proposed. The fact is, the vast majority of skaters even the very best ones aren't capable of consistently landing and changing up all their combos like that. What is important about the 3/3 penalty is how it discourages risk and how it shapes the new generation of skaters. We don't need to invent hypotheticals, we have living examples of all this in action.

For instance, the example I keep trotting up of how higher quality, higher difficulty jumping passes of a 3lutz/3toe and a 2axel would only be .1 ahead of a lesser quality 2axel/3toe and high quality 3lutz due to the scale of values is not a hypothetical. I'm basing it on Yuna Kim vs. Miki Ando, skaters who do both those jumping passes often with that resulting GOE (although Yuna has yet to do hers under the new values in the COP). This will likely come into play at the upcoming worlds and it is patently unfair. It doesn't matter if there's a chance it'll be made up for in PCS, because that would be a misuse of PCS. The COP is supposed to remove the guesswork of how degrees of difficulty will directly translate into points, not make skaters guess.

And I don't think skaters are guessing. I don't know if there are skaters who outright admit that they're doing the 2axel/3toe combo this season to take advantage of the COP's negligence (dorispulaski pointed out that Virtue/Moir admitted to a similar strategy with lifts in ice dancing), but we can see the results. And the fact is a lot of ladies skaters are now doing 2axel/3toes and not attempting any 3/3s even though the UR penalty has gone down.

This is also having a troublesome effect on the next generation of skaters. For instance, the two rising Japanese junior ladies: Risa Shoji and Miyabi Oba. Both those ladies have beautiful and consistent 3/3s, the 3sal/3toe. They've landed it multiple times in the SP this season with no UR calls and all +GOE. And yet neither of them attempt the 3/3 in their FS, even though there's more room for error in the FS. Instead, they both stick to a 2axel/3toe in the FS, and in Oba's case, downgrade her 3s/3t to a 3s/2t. Why aren't they doing the most difficult jumping passes that they're so consistent on in their FS, even though they could? The only plausible explanation is strategic scoring due to the COP. They're relegating their most difficult combo to the SP because that's the only place where it has definitive strategic value (no axel combos possible there, and a 3/3 in the SP allows a skater to slip in an extra triple in the SP without doing a 3axel).

And the strategy is rewarded: in the recent World Juniors competition, Risa Shoji got +.7 Goe for her 3s/3t and +.43 for her 2axel in the SP, while she got +.9 for her 2axel/3toe and +.6 for her 3sal in the FS, that's a higher GOE for less difficult jump combos with the same base value.

This is wrong. The fact that these two skaters can do a more difficult combo should be rewarded, not discouraged. They shouldn't have to hold back on doing a more difficult combo that they're perfectly capable of. This system is shaping the next generation of skaters in the wrong way.

I believe my proposition still holds for layouts that don't have triple-triple sequences.

I think Wallylutz' example

1) 3Lz
2) 3F+3Lo
3) 2A+3T
4) 3Lz+1Lo*+3S
5) 3F
6) 2A
7) 2Lz

does defeat the original proposition, and it contains no sequences (unless you are usng the word "sequence" here in a different way thatn the official rules do.)

Even in this example, though, it is possible to eliminate one of the two triple-triples, but not both, by rearranging the jumps. The rearrangement in this example has the same base value, and gives the possibility of +3 GOE for six of the seven passes (instead of five of the seven), but even so it is not "easier" because it requires the very difficult 3Lz+1Lo+3F.

I think the right version of your theorem would be to include the extra assumption that the original layout does not contain a cembination that has a triple jump and also a do7ble Axel. This theorem can probably be strengthened, but this is the version that your original proof addresses.

Watch the weaker juniors and novices and below who don't do triple jumps, and maybe you'll occasionally see double something easier than axel-double salchow combinations with the first jump landed on an inside edge. Still rare, but it has been done in the past so more likely it'll be done again in the near future.

Triple Salchow double flip! Holy wow--so any jump could be allowed to land on the inside edge of the opposite foot in order add a salchow or flip in combination!?

Triple Salchow double flip! Holy wow--so any jump could be allowed to land on the inside edge of the opposite foot in order add a salchow or flip in combination!?

It's allowed.
The question is whether any skater can do it well enough to be worth more than an easier or or more typical combination done with better quality.

Originally Posted by Krislite

By triple-triple sequence I meant of the kind: 3+half-loop+3. I realize the new rules count this as a combo, but I don't think it's valid to call it triple-triple combo. So what should we call it?

Triple-single-triple combo? Three-jump combo with half-loop and two triples?

You need to distinguish between something like 2A+2A+SEQ (double axel, step forward or tap toe, double axel) or 3S+3T+SEQ (triple sal, hop hop hop, triple toe), which are worth less than their base value because of the 0.8 sequence multiplier.

3+half loop+3 no longer gets the sequence penalty, so it's a much more attractive choice than it was last year.

Very creative attempt, I am impressed! But you know me, I am never easy. I am going to hit you back with this:

1) 3Lz+3Lo
2) 3A+3T
3) 3F
4) 2A+1Lo*+3S
5) 3A
6) 3Lz
7) 2A

By making the two repeated jumps = Axel and Lutz as the two Triple jump types that cannot be connected in a combo, this now kills your theorem as well. Now, before you jump at me and claim a woman cannot do 3A+3T , I have this concrete evidence to support it as viable option for women: http://www.youtube.com/watch?v=3e9g_...eature=related However, I do not believe a woman has ever done 3Lz+half Loop+3F so your layout, while passable in theory, is not a practical layout or viable option vs. the one you sought to replace. Essentially, by trying to eliminate one of the two Triple-Triple combos in my layout, you ended up increasing the overall difficulty level of the entire program through a theoretical jump combination so difficult that defeats the original purpose, which was to reduce the risk and increase GOE earning potential. In any event, now I just gave you a revised layout that cannot be connected even in theory, your hands are now tied, even as a math genius.

But Mao could do even better (same base value and possibly a tenth or two of "potential " GOE?) by replacing one of the 3 flip combos with 2A+3Lo and replacing the solo 2A with solo 3F, which I believe was Krislite's original point. So I don't see the CoP incentive for doing two triple-triple combos instead of an Axel-triple combo in this set-up.

Ah, I see why you didn't get my intention. Because I don't believe the tiny little "GOE Potential" is real. It's only a possibility on paper and unlike say Base Value, the so called 0.2 GOE earning differential will most likely be neutralized in practice by other considerations such as the psychological weight on people watching that a program having two 3/3 is worth more than one with two 2/3. Additionally, a point gkelly brought up yesterday which is worth repeating: "Is 2A+3T necessarily easier than 3T+3T?" Frankly, the answer is no, not necessarily. It may sound counter-intuitive but only people who have experience actually doing skating jumps can relate to, that is an Axel jump creates a very unique thrust on landing that makes keeping your balance rather tricky, especially when you are trying to connect the Axel jump into another toe jump. Toe jump connects well with another toe jumps, likewise, the motion of edge jumps usually connects well with other edge jumps as well assuming no technique issues exists. But connecting edge jump into a toe jump or vice versa is almost always more tricky. It's hard to explain but there is like an additional force working against your body when you try to connect the two.

So even though 2A+3Lo is easier than 3F+3Lo in theory and there is no doubt 3F is harder than 2A and one could even say two edge jumps should connect better. The reality is Mao can benefit from a form of "economy of scale", sort to speak, by focusing on training one single type of Triple-Triple combo for both her SP and LP, it would be a very efficient use of her training time. Consistency comes from practice. If she has to worry about 3 different types of difficult 3/3 combos, that is very distracting. Yu-Na Kim only does one type of 3/3 too but she doesn't bother repeating her 3/3 because it's kind of pointless for her as she lacks enough Triple jumps in her repertoire to make the extra jumping pass worthwhile, which is her biggest weakness and this may start to catch up on her should she continue to compete with more and more ladies doing 3/3 with full repertoire of Triples. So despite what theory suggests, it makes every sense that she does two Triple Flip combinations in her FS. Her coaches understood that and you'll note, she has been doing two Triple Flip combos in her FS for sometime, that is provided she doesn't make mistakes on them. It's just that Mao is not ready to put the Triple Loop back with the Triple Flip yet. She is not ready with all the technique problems she has been having but I am very encouraged by her progress this year despite the poor international results earlier. I think once Mao finally regains her Triple Lutz, stabilizes her Salchow and get rid of the UR image re: her Triple Axel, she would then be ready to tackle & bring back the Triple Flip+Triple Loop combo. When she does, even Yu-Na Kim won't be able to touch her, not for that kind of huge point differential gap anyway, 12~13 points in BV is way too much especially now that jumps tend to earn less GOE as a whole, everything else being the same as before.